In the fourth and fifth centries AD two brilliant Chinese mathematicians togther formed a proof that is in my opponion the best method to explain in terms of simplicity. Through the use of a cube these Chinese men were able to find the volume of a sphere.

Check out the work of Liu Hui and Zhu Gengzhi.

The Great Chinese Cube Discovery


To completely understand this explanation you must understan the volome of a cone. The volume of the cone starts with knowing the area of the base of the cone. This is simply the area of the circle.

Take a look at this video on the volume of the cone